The Pattern recognition framework and Hoeffding's bounds

One of the main restrictions of the PAC framework that makes it unrealistic is that the labels of the instances are assumed to be generated by a concept from a predetermined concept class. In real world applications of learning we can rarely assume such prior knowledge. A more realistic framework of analysis is the “Pattern recognition problem” framework proposed by Vapnik [5]. In this framework we make the much weaker assumption that examples are generated independently at random from some unknown distribution and that we have reason to believe that some concept from a know concept class is likely to be a good predictor of the label given the instance for this distribution. More formally, we define the interaction between the teacher and the student as follows (Compare this to the student-teacher interaction defined for the PAC framework).